In modern computer experiment applications, one often encounters the situation where various models of a physical system are considered, each implemented as a simulator on a computer. An important question in such a setting is determining the best simulator, or the best combination of simulators, to use for prediction and inference. Bayesian model averaging (BMA) and stacking are two statistical approaches used to account for model uncertainty by aggregating a set of predictions through a simple linear combination or weighted average. Bayesian model mixing (BMM) extends these ideas to capture the localized behavior of each simulator by defining input-dependent weights. One possibility is to define the relationship between inputs and the weight functions using a flexible non-parametric model that learns the local strengths and weaknesses of each simulator. This paper proposes a BMM model based on Bayesian Additive Regression Trees (BART). The proposed methodology is applied to combine predictions from Effective Field Theories (EFTs) associated with a motivating nuclear physics application.
翻译:在现代计算机实验应用中,人们常常遇到一种情况,即考虑物理系统的各种模型,每个模型都作为模拟器在计算机上执行。在这种环境下,一个重要的问题是确定用于预测和推断的最佳模拟器或模拟器的最佳组合。巴伊西亚平均模型(BMA)和堆叠是两种统计方法,用来通过简单的线性组合或加权平均值汇总一套预测来计算模型的不确定性。巴伊西亚模型混合(BMM)将这些想法扩大到通过界定依赖输入的重量来捕捉每个模拟器的局部行为。一种可能性是使用一种灵活的非参数模型来界定投入和重量函数之间的关系,该模型可以了解每个模拟器的当地强弱。本文提出了一种基于Bayesian Additive Regrestiion 树(BART)的BMM模型。拟议方法用于结合与激励性核物理应用有关的有效战场理论(EFTs)的预测。